$A$ rectangular coil $20\,cm \times 20\,cm$ has $100$ turns and carries a current of $1\,A$. It is placed in a uniform magnetic field $B = 0.5\,T$ with the direction of the magnetic field parallel to the plane of the coil. The magnitude of the torque required to hold this coil in this position is ........ $N-m$.

$A$ circular coil of $30$ turns and radius $8.0\, cm$ carrying a current of $6.0\, A$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0\, T$. The field lines make an angle of $60^o$ with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning. (in $, Nm$)

$A$ circular coil carrying a current of $2.5 \ A$ is free to rotate about an axis in its plane perpendicular to an external magnetic field. When the coil is made to oscillate,the time period of oscillation is $T$. If the current through the coil is $10 \ A$,the time period of oscillation is

If $m$ is the magnetic moment and $B$ is the magnetic field,then the torque is given by

$A$ current-carrying loop is free to turn in a uniform magnetic field. The loop will come into equilibrium when its plane is inclined at

Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of
$(i)$ electric dipole $\vec{p}$ in an electrostatic field $\vec{E}$ and
$(ii)$ magnetic dipole $\vec{M}$ in a magnetic field $\vec{B}$. Write down a set of conditions on $\vec{E}, \vec{B}, \vec{p}, \vec{M}$ so that the two motions are verified to be identical. (Assume identical initial conditions.)